Page 89 - Geothermal Energy Renewable Energy and The Environment

74 Geothermal Energy: Renewable Energy and the Environment

acTiviTy, a
The way in which the chemical potentials of components change in response to changes in pressure
and temperature or other state variables is represented by the activity. Activity is a thermodynamic
measure of the difference between the chemical potential of a component in a phase from one set of
conditions to another. This change in chemical potential follows the form

0
μ i T,P,x = μ + R × T × ln (a), (5.3)
i
i
where μ i T,P,x is the chemical potential of component i at some pressure, temperature, and composi-
tion (x) of the phase being considered and μ is the chemical potential of component i at some stan-
0
i
dard state, including a reference composition. Then, by analogy with Equations 5.1 and 5.2,
i0
∆G = ∑μ j iT,P,x = ∑ [μ + R × T × ln (a )], (5.4)
i
j
j
j
∆G = ∑ ∆G . (5.5)
rx
j
These relationships provide the means to determine the chemical state of a system from the
chemical compositions of the phases in the system. They also provide a means to predict the behav-
ior of a system when it is subjected to conditions different from those that determined its current
compositional features. Conversely, and importantly for considerations regarding geothermal sys-
tems, the chemical composition of phases in a system contain information about the temperature
and pressure the system has experienced. We will exploit this fact when we consider exploration for
geothermal systems in Chapter 6.

saTUraTIon and The law oF mass acTIon
Let us return to that pot of boiling water we considered in Chapter 2. Assume that once the pot is
boiling we immediately remove it from the stove and place it in a perfectly insulated container.
Just before we close the container and isolate the pot from the rest of the world, we pour in exactly
10 grams each of table salt (i.e., halite, NaCl) and quartz sand (SiO ), both of which have been
2
ground to a particle size in which every particle has a diameter of exactly 10 microns. If we open
the container 10 minutes later, what would we find? An hour later? A day later? If we opened it a
year later, would it be any different?

equilibrium consTanTs
Experience would say that the salt would dissolve relatively quickly, eventually completely disap-
pearing. But, would it be gone after 10 minutes? And, if we kept adding 10 gram aliquots of salt,
how much salt could be added to the 100°C water before no more would dissolve? Would the quartz
eventually dissolve completely, too? Would it do so in the same amount of time?
The answers to these questions are determined by the so-called law of mass action and reaction
rate laws. The law of mass action relates to chemical reactions that have achieved equilibrium. Take,
for example, the dissolution of halite, which can be written as a chemical reaction in which the halite
is the reactant and the ions in solution are the products,

NaCl < = > Na + Cl .
+
–
Note that electrical neutrality is perfectly maintained when halite is dissolved; all complete
reactions must conform to this necessity. At equilibrium, the reaction proceeds in both directions